In vision science it is common to represent errors of the eye as wavefront aberrations. When doing this, there are various kinds of mathematical representations that can be used. In particular, polynomials, such as the Zernike polynomials, are well suited for this purpose and are frequently used. In general, the Zernike polynomials describe defects that are departures from perfect imagery. More specifically, they describe the properties of an aberrated wavefront, and do so without regard to the symmetrical properties of the system that gave rise to the wavefront.
Mathematically, the Zernike polynomials are usually defined in polar coordinates Z(ρ,θ), where ρ is the radial coordinate ranging from 0 to 1, and θ is the azimuthal component ranging from 0 to 2π. Typically, each Zernike polynomial consists of three components. These are: a normalization factor, a radial dependent component, and an azimuthal dependent component. In this context, the radial component is a polynomial, whereas the azimuthal component is sinusoidal.
With the above in mind, a wavefront description using Zernike polynomials can be given in the general form:W(ρ,θ)=ΣcnmZnm(ρ,θ,αnm)
In the above expression, “n” pertains to the order of the polynomial (i.e. 2nd or 3rd order aberration) and “m” pertains to frequency (i.e. θ, 2θ, and 3θ). Further, cnm is a coefficient that pertains to magnitude; and Znm(ρ,θ,αnm) depends on radial and azimuthal considerations as they relate to a particular axis (αnm).
When considering the human eye as a genuine optical system, aberrations can be generally categorized as being either symmetric or asymmetric with respect to the optical axis of the eye. For this categorization, symmetrical aberrations are radially symmetrical with respect to the optical axis, while the asymmetrical aberrations are not. As indicated by the Zernike polynomials, in addition to their symmetry or lack thereof the various optical aberrations of the eye can be categorized by their order. Insofar as imaging is concerned, it happens that the so-called lower order aberrations (i.e. 2nd, 3rd and 4th order) can be significantly detrimental. These lower order aberrations include both symmetrical and asymmetrical aberrations.
Perhaps, the most well known aberrations of a human eye are myopia, hyperopia and astigmatism. All are 2nd order aberrations, according to the Zernike polynomials, but of these, only astigmatism is an asymmetrical aberration. Heretofore, these aberrations have been corrected by glasses, contact lenses, or eximer-laser-surgery, without directly considering the effects of other aberrations. Along with the 2nd order aberrations just mentioned, however, additional asymmetrical aberrations in the 3rd and 4th orders can also be significantly detrimental to human vision. This is particularly so under relatively poor lighting conditions. Indeed, aside from the effects caused by myopia and hyperopia, it is estimated that of the remaining detrimental effect on vision, 85% is caused by the 2nd and 3rd order asymmetrical aberrations (i.e. astigmatism, coma and trefoil), 10% is caused by the symmetrical 4th order spherical aberration, while only about 5% result from the remaining higher order aberrations. In any event, when vision correction is undertaken, it is clear that a compensation for as many aberrations as possible would be beneficial.
With the above in mind, the aberrations of interest here are the asymmetrical aberrations that include: astigmatism (Z3 and Z5; 2nd order), coma (Z7 and Z8; 3rd order) and trefoil (Z6 and Z9; 3rd order). Using the Zernike polynomials, each asymmetrical aberration can be modeled individually for each patient. Importantly, this modeling can be done as pairs of identical patterns. Further, the pair of patterns for a particular asymmetrical aberration (e.g. coma) are patient specific. In each instance, the patterns for a particular asymmetrical aberration will have a common orthogonal axis. Each pattern, however, will have a different rotational alignment around this common axis. Stated differently, there will be an angle of rotation “α” between the patterns of an asymmetrical aberration. Again, the angle “α” will be patient specific and it will determine the magnitude of the aberration. Thus, for each patient, a model for each asymmetrical aberration (e.g. astigmatism, coma, and trefoil) will have respective patterns, and will have a respective angle “α” between the patterns.
In light of the above it is an object of the present invention to provide adaptive optics that model asymmetrical aberrations of the eye in accordance with appropriate Zernike polynomials to compensate for the asymmetrical aberrations that are introduced by a human eye in an imaging process. Yet another object of the present invention is to provide an optical device that helps minimize the detrimental effects on vision that are caused by asymmetrical aberrations induced by a human eye. Still another object of the present invention is to compensate for asymmetrical aberrations by providing adaptive optics that are easy to use, simple to assemble, and comparatively cost effective.